Slip-regulated vehicle brake systems usually comprise a piston pump as a hydraulic pump that produces pressure oscillations in transported brake fluid owing to the pulsating delivery manner thereof. For damping the pressure oscillations, it is known to connect a pressure variation damper to a pressure side of the piston pump that damps the pressure variations when transporting the brake fluid with the piston pump and as a result reduces the noise generation and the reaction on a master brake cylinder and thereby on a foot brake pedal or a hand brake pedal. Besides this, the damping of the pressure oscillations in the brake fluid improves the quality of the control of the slip regulation.